Approximate method for eigensensitivity analysis of a defective matrix

Based on the exact modal expansion method, an arbitrary high-order approximate method is developed for calculating the second-order eigenvalue derivatives and the first-order eigenvector derivatives of a defective matrix. The numerical example shows the validity of the method. If the different eigenvalues μ(1),…,μ(q)μ(1),…,μ(q) of the matrix are arranged so that |μ(1)|≤⋯≤|μ(q)||μ(1)|≤⋯≤|μ(q)| and satisfy the condition that |μ(q1)|<|μ(q1+1)||μ(q1)|<|μ(q1+1)| for some q1